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A coordinate covalent will occur between a Lewis acid and a Lewis base (think of NH3 or F- sharing a pair of electrons). A polar covalent bond is when one electron is shared between two atoms; polar describes the ionic character of the bond. More electrons in the electron cloud will be pulled towards the atom with a higher electronegativity, so the polar covalent bond has more ionic character than a nonpolar covalent bond.
Covalent bonding occurs between two atoms that share electrons in order to complete each other's octet. With coordinate covalent bonding, a lewis base will coordinate covalently bond to a lewis acid and provide all of the electrons needed to complete the lewis acid's octet. In this case, the lewis acid is not sharing any of its electrons and instead requires the donation of all the electrons needed to complete its octet.
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